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Real v e r sus Nominal Rates. You will receive \$100 from a savings bond in 3 years. The nominal interest rate is 8 percent. a. What is the present value of the proceeds from the bond? b. If the inflation rate over the next few years is expected to be 3 percent, what will the real value of the \$100 payoff be in terms of todays dollars? c. What is the real interest rate? d. Show that the real payoff from the bond (from part b) discounted at the real interest rate (from part c) gives the same present value for the bond as you found in part a.
Given that we will receive 100 dollars from savings bond in three years. Nominal Interest Rate = 8% a. What is the present value of the proceeds from the bond? Ans. Amount to be received \$ 100.00 Time period in years 3 Nominal interest rate 8.00% Inflation rate 3.00% The present value can be calculated using the formula Present Value = Amount / (1+i)^n =100/(1+8%)^3 \$79.38 b. If the inflation rate over the next few years is expected to be 3%, what will the real value of the \$100 payoff be in terms of todays dollars? Ans. The real value can be calculated using the below formula Real Value = Amount / (1+inflation)^n =100/(1+3%)^3 \$91.51 c. What is the real interest rate? Ans. The real interest rate can be calcuated using the formula as below Real Interest = ((1+rate)/(1+inflation))-1 =((1+8%)/(1+3%))-1 4.854% d. Show that the real payoff from the bond (from…

part b) discounted at the real interest rate (from part c) gives the same present value for the bond as you found in part a. The real payoff from the bond as calculated in part b = \$91.51 Real Interest calculated in part c = 4.854% The present value can be calculated using the formula as below Present Value = Amount /(1+real interst)^n =91.51/(1+4.854%)^3 79.3804483 This is same as the answer we found in part a Therefore, the real payoff from the bond (from part b) discounted at the real interest rate (from part c) gives the same present value for the bond as found in part a.

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